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Transformation Of Functions

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1. Draw the graph of y=f(x) where f(x)=x^2

Describe the transformation which maps y=f(x) to y=f(x-2)

For this I would basically have to draw the graph x^2 and move the graph 2 places to the right.

The thing is that I don't understand why are we moving the vertex two places to the right.
2. f(0) = 0

In the original graph x=0 gives f(0)
In the second graph x=2 gives f(0)
3. (Original post by TenOfThem)
f(0) = 0

In the original graph x=0 gives f(0)
In the second graph x=2 gives f(0)
I'm not following.

Why are you doing x=2 and what are you trying to show by f(x)=0
4. (Original post by zed963)
I'm not following.

Why are you doing x=2 and what are you trying to show by f(x)=0
You asked why the vertex moved 2 places to the right

The vertex of the original graph is (0,0)

The vertex of the translated graph is (2,0)
5. Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2
6. (Original post by zed963)
Are you trying to say that to make x=0 what do I need to do to make it 0 so in this case add 2
no
I am saying that to get the vertex in the transformed graph x=2

f(2-2) = 0
7. (Original post by TenOfThem)
no
I am saying that to get the vertex in the transformed graph x=2

f(2-2) = 0
Understood.
8. So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

So if I had f(-x) or -f(x)

What determines which one I choose
9. (Original post by zed963)
So how do I know which one I should choose for example if I was shown a graph and it told me to state the function and I had two choices to choose from which One would I choose.

So if I had f(-x) or -f(x)

What determines which one I choose
Wether the x has changed [f(-x)] or the y has changed [-f(x)]

The former transforms parallel to the x-axis whereas the latter transforms parallel to the y-axis

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